Analysis of the motion of 2-dimensional patterns: evidence for a second-order process.

The sum of two differently orientated moving sinusoidal gratings of similar spatial frequency, contrast, and velocity appears as a single coherent "plaid" pattern. The visual system is thought to analyse the motion of plaids in two stages, first analysing the motion of the (1-D) components, and then calculating a speed and direction which is consistent with those 1-D motions. We studied the apparent direction of motion of plaids made by adding two components that had the same spatial frequency and contrast, and were symmetrically oriented about the vertical axis. The gratings moved in jumps, and we studied the effect of varying the size of the jump, the angle between the component gratings, and the temporal interval between the jumps, on the perceived direction of motion. When the size of the jumps was increased to 3/8 of their spatial period, the perceived direction of motion of the plaid pattern reversed, although if one component were presented alone, its direction of movement did not reverse. Reversed motion of this type was consistently obtained if the angle between the components was greater than about 140 degrees, if the interval between jumps was at least 25 msec, and if the spatial frequency of the component gratings was less than about 4 c/deg. When the angle between the components was smaller, or the time between jumps was greater, most observers saw normal motion in the direction predicted by the two-stage hypothesis. When the spatial frequency was raised, observers saw no consistent motion.(ABSTRACT TRUNCATED AT 250 WORDS)     

The role of color in the motion system.

We have examined the ability of observers to determine the direction of movement of a variety of colored plaid patterns. When the two plaid components are of unequal spatial frequency or of unequal luminance or chromatic contrast, observers judge the direction of movement incorrectly. These errors are correlated with a misjudgement of the speeds of the two components. Our results provide support for an initial decomposition into oriented components followed by a subsequent component-to-pattern recombination of moving equiluminant and colored plaids. At equal multiples of threshold contrast a moving luminance grating is about 8 times more powerful than a moving equiluminant grating in determining the apparent direction of motion of a plaid. When both are present, luminance and color do not interact linearly. Color and motion must be processed in parallel in at least partially separate pathways.     

Two-dimensional pattern motion analysis uses local features

Extensive research suggests that the visual system computes the direction of motion of a two-dimensional pattern from the motion of its oriented spatial frequency components. However, there is some evidence to suggest that the local features in a pattern are also important. In order to demonstrate that the local features contribute to motion perception we have created complex stimuli in which the oriented spatial frequency components have the same direction of motion but the local features move in different directions. The stimuli are multi-component plaid patterns with alternating high and low contrast rows. An analysis based on the oriented spatial frequency components predicts a uniform motion percept for the whole pattern. However, an analysis based on the local features in the pattern predicts that the high-contrast and low-contrast rows would be perceived to move in opposite directions. In a direction discrimination task, observers reported opposite directions of motion for small patches of the pattern that were centred on high and low contrast rows. This supports the hypothesis that the visual system uses local features when computing pattern motion. We show that a simple energy model with localised motion sensors that are broadly tuned for orientation could explain our results.     

Motion Coherence Across Different Chromatic Axes

It has been reported that equiluminant plaid patterns constructed from component gratings modulated along different axes of a cardinal colour space fail to create a coherent impression of two-dimensional motion Krauskopf and Farell (1990). Nature, 348, 328–331. In this paper we assess whether this lack of interaction between cardinal axes is a general finding or is instead dependent upon specific stimulus parameters. Type I and Type II plaids were made from sinusoidal components (1 cpd) each modulated along axes in a cardinal colour space and presented at equivalent perceived contrasts. The spatial angular difference between the two components was varied from 5 to 90 deg whilst keeping the Intersection of Constraints (I.O.C.) solution of the pattern constant. Observers were required to indicate the perceived direction of motion of the pattern in a single interval direction-identification task. We find that: (i) When plaids were made from components modulated along the same cardinal axis, coherent “pattern” motion was perceived at all angular differences. As the angular difference between the components decreased in a Type II plaid, the perceived direction of motion moved closer to the I.O.C. solution and away from that predicted by the vector sum. (ii) A plaid made from components modulated along red-green and blue-yellow cardinal axes (cross-cardinal axis) did not cohere at high angular differences (>30 deg) but had a perceived direction of the fastest moving component. At lower angular differences, however, pattern motion was detected and approached the I.O.C. solution in much the same way as a same-cardinal axis Type II plaid. (iii) A plaid made from a luminance grating and a cardinal chromatic grating (red-green or blue-yellow) failed to cohere under all conditions, demonstrating that there is no interaction between luminance and chromatic cardinal axes. These results indicate that there are conditions under which red-green and blue-yellow cardinal components interact for the purposes of motion detection. Copyright © 1996 Elsevier Science Ltd.     

Two-stage analysis of the motion of 2-dimensional patterns, what is the first stage?

The sum of two differently orientated moving sinusoidal gratings of similar spatial frequency, contrast, and velocity appears as a single coherent "plaid" pattern. The visual system is thought to analyse the motion of plaids in two stages, first analysing the motion of the (1-D) components, and then calculating a speed and direction which is consistent with those 1-D motions. We find that the direction of motion of a plaid (components 1.6 c/deg orientated +60 degrees and -60 degrees) can be discriminated at velocities so low that the direction of motion of its components is not discriminable. This finding is not consistent with the "two-stage" hypothesis in the form that it is usually expressed. We suggest that mechanisms sensitive to the motion of local elements in the pattern, such as edges, could also contribute to the first stage of the analysis of plaid motion.     

Extrinsic factors in the perception of bistable motion stimuli

When viewing a drifting plaid stimulus, perceived motion alternates over time between coherent pattern motion and a transparent impression of the two component gratings. It is known that changing the intrinsic attributes of such patterns (e.g. speed, orientation and spatial frequency of components) can influence percept predominance. Here, we investigate the contribution of extrinsic factors to perception; specifically contextual motion and eye movements. In the first experiment, the percept most similar to the speed and direction of surround motion increased in dominance, implying a tuned integration process. This shift primarily involved an increase in dominance durations of the consistent percept. The second experiment measured eye movements under similar conditions. Saccades were not associated with perceptual transitions, though blink rate increased around the time of a switch. This indicates that saccades do not cause switches, yet saccades in a congruent direction might help to prolong a percept because (i) more saccades were directionally congruent with the currently reported percept than expected by chance, and (ii) when observers were asked to make deliberate eye movements along one motion axis, this increased percept reports in that direction. Overall, we find evidence that perception of bistable motion can be modulated by information from spatially adjacent regions, and changes to the retinal image caused by blinks and saccades.     

Moving two-dimensional patterns can capture the perceived directions of lower or higher spatial frequency gratings.

Coherent plaid motion is produced by superimposing two one-dimensional gratings of the same spatial frequency moving +/- 60 degrees from the intersection-of-constraints (IOC) resultant direction. These moving plaids were found to change the perceived direction of a third one-dimensional grating, either 6-fold lower or higher in spatial frequency, from traveling in one of the plaid's component direction to the IOC resultant direction. We describe this phenomenon as coherence capture. Coherence capture was found to be effective between plaids with 0.5, 1.0, and 1.5 c/deg components and gratings of 3.0, 6.0 and 9.0 c/deg respectively. It was also found to be effective between plaids with 3.0 c/deg components and gratings of 0.5 c/deg. However, coherence capture between higher spatial frequency plaids and lower spatial frequency gratings became less effective when the component spatial frequencies of the plaid increased.     

Perceived direction of plaid motion is not predicted by component speeds

It has been shown that the perceived direction of a plaid with components of unequal contrast is biased towards the direction of the higher-contrast component [Stone, L. S., Watson, A. B., & Mulligan, J. B. (1990). Effect of contrast on the perceived direction of a moving plaid. Vision Research 30, 1049-1067]. It was proposed that this effect is due to the influence of contrast on the perceived speed of the plaid components. This led to the conclusion that perceived plaid direction is computed by the intersection of constraints (IOC) of the perceived speed of the components rather than their physical speeds. We tested this proposal at a wider range of component speeds (2-16deg/s) than used previously, across which the effect of contrast on perceived speed is seen to reverse. We find that across this range, perceived plaid direction cannot be predicted either by a model which takes the IOC of physical or perceived component speed. Our results are consistent with an explanation of 2D motion perception proposed by [Bowns, L. (1996). Evidence for a feature tracking explanation of why Type II plaids move in the vector sum direction at short durations. Vision Research, 36, 3685-3694.] in which the motion of the zero-crossing edges of the features in the stimulus contribute to the perceived direction of motion.     

Evidence for a Feature Tracking Explanation of Why Type II Plaids Move in the Vector Sum Direction at Short Durations

When two moving sinusoidal gratings, with similar spatial frequency, contrast, phase, but different orientation are combined to form a plaid, their perceived direction of motion has been predicted by the intersection of constraints rule (IOC) (Adelson & Movshon, Nature, 300, 523–525, 1982). However, at short durations (60 msec) the direction of perceived motion has been predicted by the vector sum direction for “Type II” plaids (Yo & Wilson, Vision Research, 32, 1, 1992). Type II plaids are the set of plaids where the components are both located on one side of the resultant computed using the IOC rule. Yo and Wilson suggest that the vector sum direction is observed for Type II plaids at short durations because non-Fourier information is not available and direction is computed from Fourier information only. The first experiment in this study replicates the original Yo and Wilson result using similar stimuli but a simpler task; perceived direction was measured using a direction discrimination task instead of the method of adjustment used by Yo and Wilson. The second experiment provides evidence against generalizing the result to all Type II plaids. A systematic set of type II plaids that varied only in terms of the orientation of the second component provided an ideal set because their predicted motion direction followed very different patterns when predicted by the IOC and vector sum computations. The results obtained were predicted more accurately by the IOC than the vector sum. Experiment 3 provides further evidence that movement in the vector sum direction is not a general property of type II plaids. A small change to the velocity of one of the components of a plaid previously perceived in the vector sum direction had the effect of shifting the perceived motion in the IOC direction, despite increasing the difference between the IOC and VS predictions. This result is not consistent with Yo and Wilson's hypothesis that Type II plaids move in the vector sum direction because of a temporal delay between Fourier and non-Fourier information. Computational analysis of the stimuli used in both the current and original experiments revealed a possible explanation of the results in terms of a contribution from local feature tracking rather than a vector sum operation. Copyright © 1996 Elsevier Science Ltd.     

Illusory position shift induced by plaid motion

In the motion-induced position shift (MIPS), the position of a moving pattern tapered by a stationary envelope is perceived to shift in the direction of the motion. It was found that plaid motion also elicited a MIPS in the direction of global motion and this global MIPS could not be predicted by the average of the local MIPSs due to component motions. We also used a pseudo plaid pattern and again observed a global MIPS that could not be predicted by the local MIPSs due to the components of the pseudo plaid pattern. We suggest the possibility that the receptive-field positions of global motion detectors shift in the direction opposite to global motion, resulting in a positional displacement in activation via population coding.     

Bivectorial transparent stimuli simultaneously adapt mechanisms at different levels of the motion pathway

The motion aftereffect (MAE) to drifting bivectorial stimuli, such as plaids, is usually univectorial and in a direction opposite to the pattern direction of the plaid. This is true for plaids that are perceived as coherent, but also for other plaids which are seen as transparent for most or all of the adaptation period. The underlying mechanisms of this MAE are still not well understood. In order to assess these mechanisms further, we measured static and dynamic MAEs and their interocular transfer (IOT). Adaptation stimuli were plaids with small (coherent) and large (transparent) angles between the directions of the component gratings and a horizontal grating, which were adjusted in spatial frequency and drift velocity so that the pattern speed and vertical periodicity remained constant. Test stimuli were horizontal static or counterphasing gratings with the same periodicity as the adaptation stimuli. MAE duration was measured for monocular, binocular and IOT conditions. All static MAEs were smallest for the transparent plaid and largest for the grating, while all dynamic MAEs were constant across adaptation stimuli. IOT was twice as big for dynamic MAEs as for static MAEs, and did not vary with the adaptation stimuli. Other adaptation stimuli were plaids that differed in intersection luminance, contrast or spatial frequency, resulting in different amounts of perceived coherence. MAEs and IOT did not vary with perceived coherence. The results suggest that the MAE for bivectorial stimuli consists of low-level adaptation (dependent on local component properties, small IOT), as well as high-level adaptation (dependent on global integrated pattern properties, large IOT), which can be measured independently with static and dynamic test stimuli.     

Plaid perception is only subtly impaired in strabismic amblyopia

Amblyopes exhibit a global motion anomaly that implicates processing beyond the local motion analysis of V1 possibly involving areas MT and MST in the extra-striate cortex. Here, we sought to further investigate this deficit by measuring the perception of moving plaid stimuli by amblyopic observers, since there is good physiological evidence that the motion of such stimuli is determined by processes beyond V1. The conditions under which the two moving components constituting the plaids were seen to cohere or move transparently over one another were investigated by manipulating their relative spatial frequencies. Percepts were measured using both short presentation durations, where both the percept and the direction of motion were reported, and long presentation durations where the bi-stability of the stimulus was directly measured. In addition, we measured the ability of amblyopic eyes to perceive globally coherent motion in a multiple aperture stimulus. We found a small increased tendency for both amblyopic and fellow-fixing eyes to perceive short duration plaid stimuli as coherent relative to control eyes, but no difference for long duration plaids. In addition, amblyopic eyes saw less coherence in multiple aperture stimuli than fellow-fixing eyes but were not reliably different from control eyes. We therefore conclude that the neural mechanisms underlying plaid perception are only subtly abnormal in amblyopia.     

Direction specific masking and the analysis of motion in two dimensions

We measured the effects of moving two-component cosine grating masks on the detectability of a moving spatially localized test pattern with a 1.0 octave spatial frequency bandwidth. Masking was used to distinguish between two-component patterns with fluid motion (blobs) and those with rigid motion (plaids). The two gratings which made up the two-dimensional masking patterns were always of the same spatial frequency and contrast, but moved in different directions. We find that plaid masks consistently produced threshold elevations that are 2.0-4.0 times greater than are produced by a single component mask at twice the contrast. Furthermore, this effect is nearly independent of the angle between the two mask components. For fluid motion, however, masking is determined by the mask component whose direction of motion is closest to that of the test. The results obtained with moving two-dimensional patterns demonstrate that, for blobs, the motion of the pattern as a whole has no effect on the degree of masking, whereas, for plaids, the signals arising from the two components interact in a nonlinear manner, thus producing a substantial enhancement of masking, which is clearly related to the coherent motion of the entire pattern. These data shed light on the properties of higher order motion units (possibly in MT cortex) that respond to the direction of two-dimensional pattern motion, suggesting that they combine, in a nonlinear manner, the outputs of units which respond independently to the direction of each mask component.     

Computational models of coherent and transparent plaid motion

The perceived motion of two added sinusoidal gratings of similar amplitude and spatial frequency but different orientations is often coherent. However, when either relative grating contrast or frequency are varied, perception may transform to a motion transparency. For plaids, both multiplicative and additive transparent percepts are reported. To explain perception, several computational models of motion transparency are proposed. The most general model considered is, however, a quadratic form with five unknowns. To stabilize the transparent model, additional constraints are introduced so that two velocities may be detected from the motion of plaid patterns. It is shown how this model may be realised by a two-layer (linear) feedforward network and how network learning paradigms may be used to explain some facets of visual perception. To describe the motion of plaid patterns there is an ambiguity because computational models of both coherent and transparent motion may be used to detect image velocity. In view of this competition between models, the issue of model selection is addressed; especially for cases where two or more models fit the image measurements without a residual error. The computational approach that is proposed affords one explanation why perception selects transparency in favour of coherence for plaid patterns by adjustments of relative grating contrast and frequency.     

Lower threshold of motion for one and two dimensional patterns in central and peripheral vision.

Lower motion thresholds for discriminating opposing motion directions were compared for one dimensional (grating) and two dimensional (plaid) stimuli in central and peripheral vision. The results were consistent with a two-stage model of motion sensitivity in which threshold-limiting noise occurs at both stages, and the speed as well as the direction of the resultant motion is determined by intersection-of-constraints (IOC) from the component motions. The results do not support a purely geometric interpretation of the IOC model, in which thresholds for plaid stimuli are related to thresholds of component gratings by a geometric factor. Neither do the data favour explanations in which local luminance features (i.e. blobs) are detected and their velocity determined. Monte-Carlo simulations of the two-stage process predict thresholds across variations in component direction, contrast, and visual field eccentricity. Lower motion thresholds for gratings and plaids both follow a saturating function of contrast; the fit between grating and plaid data is improved when the plaid contrast is expressed in terms of the contrast of its components. Although less contrast saturation was found in the periphery, in relative terms, plaid and grating motion thresholds were similar in central and peripheral vision, implying cortical magnifications are similar for mechanisms which process grating and plaid motion.     

Local velocity representation: evidence from motion adaptation

Adaptation to a moving visual pattern induces shifts in the perceived motion of subsequently viewed moving patterns. Explanations of such effects are typically based on adaptation-induced sensitivity changes in spatio-temporal frequency tuned mechanisms (STFMs). An alternative hypothesis is that adaptation occurs in mechanisms that independently encode direction and speed (DSMs). Yet a third possibility is that adaptation occurs in mechanisms that encode 2D pattern velocity (VMs). We performed a series of psychophysical experiments to examine predictions made by each of the three hypotheses. The results indicate that: (1) adaptation-induced shifts are relatively independent of spatial pattern of both adapting and test stimuli; (2) the shift in perceived direction of motion of a plaid stimulus after adaptation to a grating indicates a shift in the motion of the plaid pattern, and not a shift in the motion of the plaid components; and (3) the 2D pattern of shift in perceived velocity radiates away from the adaptation velocity, and is inseparable in speed and direction of motion. Taken together, these results are most consistent with the VM adaptation hypothesis.     

Computing feature motion without feature detectors: a model for terminator motion without end-stopped cells.

Pointlike object features such as line-endings, have a privileged position in the computation of the veridical direction of object motion. Experiments confirm that the human visual system relies heavily on such features if they are present. It has been proposed that units such as end-stopped cells might be necessary for the computation of feature motion instead of the simple cells used in plaid motion models. Conventional plaid motion models have not been applied to feature motion. We present here a model, based on ordinary simple cells, using two parallel pathways (Fourier and non-Fourier) for the computation of the direction of two dimensional motion. Although similar in structure to popular models of plaid motion, our model includes a novel scheme for contrast normalisation and incorporates spatial pooling at the level of MT cells. The model predictions are consistent with psychophysical results for plaids. Furthermore, it computes directions within 5 degrees of the physical motion of line-endings. It is shown that the non-Fourier signal is necessary for the computation of veridical motion.     

The oblique plaid effect

Plaids are ambiguous stimuli that can be perceived either as a coherent pattern moving rigidly or as two gratings sliding over each other. Here we report a new factor that affects the relative strength of coherency versus transparency: the global direction of motion of the plaid. Plaids moving in oblique directions are perceived as sliding more frequently than plaids moving in cardinal directions. We term this the oblique plaid effect. There is also a difference between the two cardinal directions: for most observers, plaids moving in horizontal directions cohere more than plaids moving in vertical directions. Two measures were used to quantify the relative strength of coherency vs. transparency: C/[C+T] and RTtransp. Those measures were derived from dynamics data obtained in long-duration trials (>1 min) where observers continually indicated their percept. The perception of plaids is bi-stable: over time it alternates between coherency and transparency, and the dynamics data reveal the relative strength of the two interpretations [Vision Research 43 (2003) 531]. C/[C+T] is the relative cumulative time spent perceiving coherency; RTtransp is the time between stimulus onset and the first report of transparency. The dynamics-based measures quantify the relative strength of coherency over a wider range of parameters than brief-presentation 2AFC methods, and exposed an oblique plaid effect in the entire range tested. There was no interaction between the effect of the global direction of motion and the effect of gratings' orientations. Thus, the oblique plaid effect is due to anisotropies inherent to motion mechanisms, not a bi-product of orientation anisotropies. The strong effect of a plaid's global direction on its tendency to cohere imposes new and important constraints on models of motion integration and transparency. Models that rely solely on relative differences in directions and/or orientations in the stimulus cannot predict our results. Instead, models should take into account anisotropies in the neuronal populations that represent the coherent percept (integrated motion) and those that represent the transparent percept (segmented motion). Furthermore, the oblique plaid effect could be used to test whether neuronal populations supposed to be involved in plaid perception display tuning biases in favor of cardinal directions.     

The Barberplaid Illusion: Plaid Motion is Biased by Elongated Apertures

The perceived direction of motion of plaids windowed by elongated spatial Gaussians is biased toward the window's long axis. The bias increases as the relative angle between the plaid motion and the long axis of the window increases, peaks at a relative angle of ≈45 deg, and then decreases. The bias increases as the window is made narrower (at fixed height) and decreases as the component spatial frequency increases (at fixed aperture size). We examine several models of human motion processing (cross-correlation, motion-energy, intersection-of-constraints, and vector-sum), and show that none of these standard models can predict our data. We conclude that spatial integration of motion signals plays a crucial role in plaid motion perception and that current models must be explicitly expanded to include such spatial interactions. Published by Elsevier Science Ltd.     

Motion energy versus position tracking: spatial, temporal, and chromatic parameters

The fundamental question in motion perception is whether motion is an interpretation imposed on an object or feature perceived at separate positions at sequential instants, or whether it is the response of direction-sensitive detectors that can extract the motion-energy in the stimulus, i.e. the orientation of spatio-temporal energy. To answer this question we constructed stimuli whose position changed in one direction while the motion energy contained in the same spatial frequency moved in the same or the opposite direction (by superimposing moving sinusoidal gratings on stationary gratings of the same spatial frequency and orientation). In every case tested (0.25-25 Hz temporal frequency; 0.25-1.0 cyc/deg spatial frequency; achromatic and equiluminant contrast), the perceived direction of motion was in the direction of motion energy, indicating the existence of neurons which compute motion direction without explicitly computing spatial position. The measurements also confirmed that motion-energy computations can be modeled as separable in spatial and temporal frequency.